Diffeomorphisms of the Klein Bottle and Projective Plane

1994/01/14 by J. S. Apps, J. S. Dowker, Apps, J. S. +1
Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Mathematics and Applications #funct-an #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.hep-th/9401068

18 pages, LATEX

arxiv created 1994/01/14 · openalex publication_date 1994/01/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate the Riemann curvature tensor and sectional curvature for the Lie group of volume-preserving diffeomorphisms of the Klein bottle and projective plane. In particular, we investigate the sign of the sectional curvature, and find a possible disagreement with a theorem of Lukatskii. We suggest an amendment to this theorem.

Related

• Curvature of Measure-Preserving Diffeomorphism Groups of Non-Orientable Surfaces
• Diffeomorphisms of Curved Manifolds
• Curvatures of Sobolev metrics on diffeomorphism groups
• Deforming Area Preserving Diffeomorphism of Surfaces by Mean Curvature Flow
• The Klein bottle in its classical shape: a further step towards a good parametrization